What is the general solution for 8cos(x)tan(x)=3tan(x) ?

The general solution for 8cos(x)tan(x)=3tan(x) is x=pin,x=1.18639…+2pin,x=2pi-1.18639…+2pin

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Popular >

8cos(x)tan(x)=3tan(x)

Solution

8 cos (x) tan (x) = 3 tan (x)

Solution

x = πn, x = 1.18639 \dots + 2 πn, x = 2 π - 1.18639 \dots + 2 πn

Degrees

x = 0^{\circ} + 18 0^{\circ} n, x = 67.97568 \dots^{\circ} + 36 0^{\circ} n, x = 292.02431 \dots^{\circ} + 36 0^{\circ} n

Solution steps

8 cos (x) tan (x) = 3 tan (x)

Subtract

3 tan (x)

from both sides

8 cos (x) tan (x) - 3 tan (x) = 0

Factor

8 cos (x) tan (x) - 3 tan (x) : tan (x) (8 cos (x) - 3)

8 cos (x) tan (x) - 3 tan (x)

Factor out common term

tan (x)

= tan (x) (8 cos (x) - 3)

tan (x) (8 cos (x) - 3) = 0

Solving each part separately

tan (x) = 0 or 8 cos (x) - 3 = 0

tan (x) = 0 : x = πn

tan (x) = 0

General solutions for

tan (x) = 0

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 0 + πn

x = 0 + πn

Solve

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

8 cos (x) - 3 = 0 : x = arccos (\frac{3}{8}) + 2 πn, x = 2 π - arccos (\frac{3}{8}) + 2 πn

8 cos (x) - 3 = 0

Move

3

to the right side

8 cos (x) - 3 = 0

Add

3

to both sides

8 cos (x) - 3 + 3 = 0 + 3

Simplify

8 cos (x) = 3

8 cos (x) = 3

Divide both sides by

8

8 cos (x) = 3

Divide both sides by

8

\frac{8 cos ( x )}{8} = \frac{3}{8}

Simplify

cos (x) = \frac{3}{8}

cos (x) = \frac{3}{8}

Apply trig inverse properties

cos (x) = \frac{3}{8}

General solutions for

cos (x) = \frac{3}{8}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

x = arccos (\frac{3}{8}) + 2 πn, x = 2 π - arccos (\frac{3}{8}) + 2 πn

x = arccos (\frac{3}{8}) + 2 πn, x = 2 π - arccos (\frac{3}{8}) + 2 πn

Combine all the solutions

x = πn, x = arccos (\frac{3}{8}) + 2 πn, x = 2 π - arccos (\frac{3}{8}) + 2 πn

Show solutions in decimal form

x = πn, x = 1.18639 \dots + 2 πn, x = 2 π - 1.18639 \dots + 2 πn

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Frequently Asked Questions (FAQ)

What is the general solution for 8cos(x)tan(x)=3tan(x) ?
The general solution for 8cos(x)tan(x)=3tan(x) is x=pin,x=1.18639…+2pin,x=2pi-1.18639…+2pin